Question

The displacement of a wave traveling in the negative y-direction is D(y,t) = ( 4.60 cm ) sin ( 6.20 y+ 60.0 t ), where y is in m and t is in s?

Answer 1

Answer:

The question is incomplete, below is the complete question

"The displacement of a wave traveling in the negative y-direction is D(y,t) = ( 4.60cm ) sin ( 6.20 y+ 60.0 t ), where y is in m and t is in s.

A) What is the frequency of this wave?

B)  What is the wavelength of this wave?

C) What is the speed of this wave?"

Answers:

a.  $f=\frac{30}{\pi }Hz$

b. $wavelength=\frac{\pi }{3.1}m$

c. $v=9.68m/s$

Explanation:

The equation of a wave is represented as

$D(x,t)=Asin(kx+wt)$

Where A=amplitude

w=angular frequency=2πf

K=wave numbers =2π/λ

since we re giving he equation  D(y,t) = ( 4.60cm ) sin ( 6.20 y+ 60.0 t ),

we can compare and get the value for the wave number and angular frequency.

By comparing we have

w=60rads/s

k=6.20

a. to determine the frequency, from the expression fr angular wave frequency we have

w=2πf hence

f=w/2π

if we substitute we arrive at

$f=\frac{60}{2\pi }\\f=\frac{30}{\pi }Hz$

b. to determine the wave length, we use

$k=\frac{2\pi }{wavelength} \\k=6.2\\wavelength=\frac{2\pi }{k} \\wavelength=\frac{2\pi }{6.2} \\wavelength=\frac{\pi }{3.1}m$

c. the wave speed  v is express as the product of the frequency and the wavelength. Hence

$v=frequency*wavelength \\v=\frac{30}{\pi } *\frac{\pi }{3.1}\\ v=9.68m/s$